Question

The cost of manufacturing a TV set is made up of material costs, labour costs and overhead costs. These costs are in the ratio 4 : 3 : 2. If materials costs and labour costs rise by 10% and 8% respectively, while the overhead costs reduce by 5%, what is the percentage increase in the total cost of the TV set ?

Answer 1

Let the cost of the T.V. be Rs x. Then,

Material cost = \(\frac{4X}{9}\), Labour cost = \(\frac{3X}{9}\), Overhead costs = \(\frac{2X}{9}\)

New material cost = \(\frac{110}{100}\)x \(\frac{4X}{9}\) = \(\frac{44X}{90}\)

New labour cost = \(\frac{108}{100}\)x \(\frac{3X}{9}\) = \(\frac{9X}{25}\)

New overhead costs= \(\frac{95}{100}\) x \(\frac{2X}{9}\) = \(\frac{19X}{90}\)

Increase in the cost of T.V. =\(\Big(\frac{44X}{90}-\frac{4X}{9}\Big)\) + \(\Big(\frac{9X}{25}-\frac{3X}{9}\Big)\)+ \(\Big(\frac{19X}{90}-\frac{2X}{9}\Big)\)

= \(\frac{4X}{90}\) + \(\frac{2X}{75}\) - \(\frac{X}{90}\) = \(\frac{20X+12X-5X}{450}\) = \(\frac{27X}{450}\)

\(\therefore\) % increase in cost = \(\frac{\frac{27X}{450}}{X}\) x 100% = \(\frac{2700}{450}\)% = 6%.